Schreier refinement theorem
In mathematics, the Schreier refinement theorem of group theory states that any two subnormal series of subgroups of a given group have equivalent refinements, where two series are equivalent if there is a bijection between their factor groups that sends each factor group to an isomorphic one.
Consider , where is the symmetric group of degree 3. There are subnormal series
contains the normal subgroup . Hence these have refinements
with factor groups isomorphic to and
with factor groups isomorphic to .
- Rotman, Joseph (1994). An introduction to the theory of groups. New York: Springer-Verlag. ISBN 0-387-94285-8.